Questions: Determine whether each table below represents y as a function of x. x -3 4 3 -2 1 -1 y 6 -3 9 -10 -3 13 This is a function False x 0 -6 -6 -5 -8 -3 y 5 -2 8 -10 -7 13 This is a function False x -10 -8 -2 -6 -9 2 y 5 -1 10 -10 20 15 This is a function True

Determine whether each table below represents y as a function of x. x -3 4 3 -2 1 -1 y 6 -3 9 -10 -3 13 This is a function False x 0 -6 -6 -5 -8 -3 y 5 -2 8 -10 -7 13 This is a function False x -10 -8 -2 -6 -9 2 y 5 -1 10 -10 20 15 This is a function True
Transcript text: (1 point) Determine whether each table below represents $y$ as a function of $x$. \begin{tabular}{|c|c|c|ccc|c|} \hline$x$ & -3 & 4 & 3 & -2 & 1 & -1 \\ \hline$y$ & 6 & -3 & 9 & -10 & -3 & 13 \\ \hline \end{tabular} This is a function False $\hat{\rightharpoonup}$ \begin{tabular}{|c|c|c|c|c|c|c|} \hline$x$ & 0 & -6 & -6 & -5 & -8 & -3 \\ \hline$y$ & 5 & -2 & 8 & -10 & -7 & 13 \\ \hline \end{tabular} This is a function $\square$ False \begin{tabular}{|r|r|r|r|r|r|r|} \hline$x$ & -10 & -8 & -2 & -6 & -9 & 2 \\ \hline$y$ & 5 & -1 & 10 & -10 & 20 & 15 \\ \hline \end{tabular} This is a function $\square$ True
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Solution

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Solution Steps

Step 1: Analyze the first table
  • The first table lists \( x \) values: \(-3, 4, 3, -2, 1, -1\).
  • The corresponding \( y \) values are: \(6, -3, 9, -10, -3, 13\).
  • Check if any \( x \) value is repeated with a different \( y \) value. Here, all \( x \) values are unique, so \( y \) is a function of \( x \).
Step 2: Analyze the second table
  • The second table lists \( x \) values: \(0, -6, -6, -5, -8, -3\).
  • The corresponding \( y \) values are: \(5, -2, 8, -10, -7, 13\).
  • Check if any \( x \) value is repeated with a different \( y \) value. Here, \( x = -6 \) appears twice with \( y = -2 \) and \( y = 8 \). Since \( x = -6 \) maps to two different \( y \) values, \( y \) is not a function of \( x \).
Step 3: Analyze the third table
  • The third table lists \( x \) values: \(-10, -8, -2, -6, -9, 2\).
  • The corresponding \( y \) values are: \(5, -1, 10, -10, 20, 15\).
  • Check if any \( x \) value is repeated with a different \( y \) value. Here, all \( x \) values are unique, so \( y \) is a function of \( x \).

Final Answer

  1. The first table represents \( y \) as a function of \( x \): \(\boxed{\text{True}}\)
  2. The second table represents \( y \) as a function of \( x \): \(\boxed{\text{False}}\)
  3. The third table represents \( y \) as a function of \( x \): \(\boxed{\text{True}}\)
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